A farm is engaged in breeding pigs. The pigs are fed on various products grown on the farm. In view of the need to ensure certain nutrient constituents (call them X,Y and Z), it is necessary to buy two additional products, say, A and B. One unit of product A contains 36 units of X, 3 units of Y, and 20 units of Z. One unit of product B contains 6 units of X, 12 units of Y and 10 units of Z. The minimum requirement of X, Y and Z is 108 units respectively. Product A costs LRs. 20 per unit and product B costs Rs. 40 per unit. Formulate the above as a linear programming problem to minimize the total cost, and solve the problem by using graphical method.

A farm is engaged in breeding hens. The hens are fed products A and B grown in the farm which contains nutrients P, Q and R. One kilogram of product A contains 36 units, 3 units and 20 units of nutrients P Q and R respectively, whereas one kilogram of product B contains 6 units, 12 units and 10 units of nutrients P, Q and R respectively. The minimum requirement of nutrients P Q and R for a hen is 108, 36 and 100 units respectively. Product A costs 20 per kilogram and product B costs 40 per kilogram. Using linear programming, find the number of kilograms of products A and B to be produced to minimize the total cost. Identify the feasible region from the rough sketch.

The unit to measure productivity is

Name the constituent units of lactose

Explain the dot product and cross product of unit vectors.

What is the cause of low farm productivity per unit in India?

The resultant of two vectors of magnitude 3 units 4 units is 1 unit. What is the value of their dot product. ?

A producer has 30 and 17 units of labour and capital respectively which he can use to produce two of goods X and Y. To produce one unit X, 2 units of labour and 3 units of capital are required. Similarly, 3 units of labour and 1 unit of capital is required to produce one unit of Y. If X and Y are priced at Rs. 100 and Rs. 120 per unit respectively to should be producer use his resources to maximize the total revenue?

A diet is to contain at leat 80 units of vitamin A and 100 units of minerals. Two foods F_(1) and F_(2) are available. Food F_(1) cost Rs. 4 per unit and F_(2) costs Rs. 6 per unit. One unit of food F_(1) contains 3 units of vitamin A and 4 units of minerals. One unit of food F_(2) contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.

A diet for a sick person must contain at least 4000 units of vitamins, 50 units of minerals and 1400 calories. Two foods X and Y are available at the cost of रु 4 and रु 3 per unit respectively. One unit of the food X contains 200 units of vitamins, 1 unit of minerals and 40 calories, whereas one unit of the food Y contains 100 units of vitamins, 2 units of minerals and 40 calories. Find what combination of X and Y should be used to have least cost, satisfying the requirements.

The prices of three commodities P ,\ Q ,\ a n d\ R are Rs x ,\ y\ a n d\ z per unit respectively. A purchases 4 units of R and sells 3 unit of P and 5 units of Qdot B purchases 3 units of Q and sells 2 units of P and 1 unit of Rdot C purchases 1 unit of P and sells 4 units of Q and 6 units of Rdot In the process A ,\ B\ a n d\ C earn Rs 6000, 5000 and 13000 respectively. If selling the units is positive earning and buying the units is negative earnings, find the price per unit of three commodities by using matrix method.